Using my body weight how do I determine the mass of planet earth?
2006-11-02 07:06:10 · 3 answers · asked by Anonymous in Science & Mathematics ➔ Physics
Use your body weight to open the door to a library.
Walk up to the reference librarian and ask "what is the mass of planet earth"?
Newton showed that, for spherical objects, you can make the simplifying assumption that all of the object's mass is concentrated at the center of the sphere. The following equation expresses the gravitational attraction that two spherical objects have on one another:
F = G * M1 * M2 / R2
R is the distance separating the two objects.
G is a constant that is 6.67259x10-11m3/s2 kg.
M1 and M2 are the two masses that are attracting each other.
F is the force of attraction between them.
Assume that Earth is one of the masses (M1) and a 1-kg sphere is the other (M2). The force between them is 9.8 kg*m/s2 -- we can calculate this force by dropping the 1-kg sphere and measuring the acceleration that the Earth's gravitational field applies to it (9.8 m/s2).
The radius of the Earth is 6,400,000 meters (6,999,125 yards). If you plug all of these values in and solve for M1, you find that the mass of the Earth is 6,000,000,000,000,000,000,000,000 kilograms (6E+24 kilograms / 1.3E+25 pounds).
1 It is "more proper" to ask about mass rather than weight because weight is a force that requires a gravitational field to determine. You can take a bowling ball and weigh it on the Earth and on the moon. The weight on the moon will be one-sixth that on the Earth, but the amount of mass is the same in both places. To weigh the Earth, we would need to know in which object's gravitational field we want to calculate the weight. The mass of the Earth, on the other hand, is a constant.
2006-11-02 07:08:42 · answer #1 · answered by DanE 7 · 0⤊ 0⤋
Your attraction to the Earth (in other words, your weight) depends on your mass, the Earth's mass, the square of the distance between you, and the gravitational constant. It can be assumed that the distance is negligible. So your mass*the Earth's mass*the gravitational constant = your weight. So your mass*the gravitational constant/your weight = the Earth's mass.
2006-11-02 15:12:08 · answer #2 · answered by Amy F 5 · 0⤊ 0⤋
y dnt u use the universal law of gravitation???
2006-11-02 15:09:34 · answer #3 · answered by karan 1 · 0⤊ 0⤋